Math
Frequency distribution
a mathematical function showing the number of instances in which a variable takes each of its possible
values.
Steps of Frequency distribution
(1) Find the range of the data: The range is the difference between the largest and the smallest values.
(2) Decide the approximate number of classes in which the data are to be grouped. There are no hard
and first rules for number of classes. In most cases we have 5 to 20 classes. H.A. Sturges provides a
formula for determining the approximation number of classes.
K=1+3.322logN
where K= Number of classes
and logN = Logarithm of the total number of observations.
Example: If the total number of observations is 50, the number of classes would be
K=1+3.322logN
K=1+3.322log50
K=1+3.322(1.69897)
K=1+5.644
K=6.644
7 classes, approximately.
(3) Determine the approximate class interval size: The size of class interval is obtained by dividing the
range of data by the number of classes and is denoted by h class interval size
(h)=RangeNumber of Classes
In the case of fractional results, the next higher whole number is taken as the size of the class interval.
(4) Decide the starting point: The lower class limit or class boundary should cover the smallest value in
the raw data. It is a multiple of class intervals.
Example: 0,5,10,15,20, etc. are commonly used.
(5) Determine the remaining class limits (boundary): When the lowest class boundary has been decided,
by adding the class interval size to the lower class boundary you can compute the upper class boundary.
The remaining lower and upper class limits may be determined by adding the class interval size
repeatedly till the largest value of the data is observed in the class.
(6) Distribute the data into respective classes: All the observations are divided into respective classes by
using the tally bar (tally mark) method, which is suitable for tabulating the observations into respective
classes. The number of tally bars is counted to get the frequency against each class. The frequency of all
the classes is noted to get the grouped data or frequency distribution of the data. The total of the
frequency columns must be equal to the number of observations.
Combination Reactions
A combination reaction is a reaction where two or more elements or compounds combine to form a
single compound. Such reactions may be represented by equations of the following form: X + Y → XY.
The combination of two or more elements and form one compound is called combination reaction.
Oxygen and the halogens are very reactive elements and are likely to undergo combination reactions
with other elements. When a metal undergos a combination reaction with oxygen, a metal oxide is
formed (similarily, a metal halide is formed if reacted with one of the halogens). You see the products of
this type of reaction whenever you see rust. Rust is the product of a combination reaction of iron and
oxygen:
Since this new compound is formed from a metal and a non-metal, it is an ionic compound. The product
will be electrically neutral and since you can predict what charge most metal ions will have based on
their location on the periodic table and oxygen will have a charge of -2, you can determine the
molecular formula for the product.
Decomposition Reaction
Defined. ... A decomposition reaction is a type of chemical reaction in which a single compound breaks
down into two or more elements or new compounds. These reactions often involve an energy source
such as heat, light, or electricity that breaks apart the bonds of compounds.
Single replacement reaction
During the reaction, A replaces B, forming the product compound AC and releasing the less reactive
element B. An example of a single replacement reaction occurs when potassium (K) reacts with water
(H2O). A colorless solid compound named potassium hydroxide (KOH) forms, and hydrogen gas (H2) is
set free.
A double-replacement reaction exchanges the cations (or the anions) of two ionic compounds. A
precipitation reaction is a double-replacement reaction in which one product is a solid precipitate.
Solubility rules are used to predict whether some double-replacement reactions will occur.